Polarization Vector for Quantum EM Field

In summary, the conversation discusses evaluating dot products involving normalized polarization vectors for single photons with specific momenta and spins. The speaker also mentions looking for identities related to these dot products and clarifies that the polarizations are along cartesian directions. Another participant mentions that the dot product result depends on the relative helicities of the photons.
  • #1
TriTertButoxy
194
0
I'm doing some calculations and I've run into something rather strange.

I need to evaluate the following dot products

[tex]\vec{\epsilon}_{k,\,s}\cdot\vec{\epsilon}_{-k,\,s'} = ?[/tex]
[tex]\vec{\epsilon}_{k,\,s}^*\cdot\vec{\epsilon}_{-k,\,s'}^* = ?[/tex]​

where [itex]\vec\epsilon_{k,\,s}[/itex] is the normalized polarization vector for a single photon with momentum [itex]k[/itex], and spin [itex]s[/itex]. Does anyone know where I can look for these identities?
 
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  • #2
Assume that the polarizations are along cartesian directions...
 
  • #3
If by "spin", you mean helicity, the e.e'=plus or minus 1, depending on the relative helicities. This works because the momenta are = and opposite.
 

What is the polarization vector for a quantum electromagnetic field?

The polarization vector for a quantum electromagnetic field is a mathematical vector that describes the direction and magnitude of the electric and magnetic fields of the quantum field. It is used to represent the polarization state of a quantum field, which determines how the field interacts with other particles and fields.

How is the polarization vector related to the classical polarization of an electromagnetic field?

The polarization vector for a quantum electromagnetic field is related to the classical polarization of an electromagnetic field through the concept of superposition. The classical polarization can be thought of as the average polarization of many quantum fields, each with different polarization vectors. In this sense, the polarization vector represents the quantum mechanical nature of the polarization state.

How does the polarization vector change in different reference frames?

The polarization vector for a quantum electromagnetic field is a Lorentz vector, meaning it transforms according to the laws of special relativity. This means that the direction and magnitude of the polarization vector will change depending on the observer's reference frame, but the overall polarization state of the field remains the same.

How is the polarization vector used in quantum field theory calculations?

In quantum field theory, the polarization vector is used to calculate the probability amplitudes for different particle interactions and scattering processes. It is also used to determine the vacuum energy and the Casimir effect, which are important phenomena in quantum field theory.

Can the polarization vector be experimentally measured?

Yes, the polarization vector of a quantum electromagnetic field can be experimentally measured using techniques such as polarimetry, which measures the polarization state of light. It can also be indirectly measured through its effects on other particles and fields in experiments.

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